Maxwell equations in complex form of Majorana–Oppenheimer, solutions with cylindric symmetry in Riemann S 3 and Lobachevsky H 3 spaces

Bogush, A. A.; Krylov, George; Ovsiyuk, Е. М.; Red'kov, V. M.

doi:10.1007/s11587-009-0067-8

Cited by 13 publications

(6 citation statements)

References 14 publications

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“…To this end, we will use an old and almost unusable in the literature approach by Riemann -Silberstein -Majorana -Oppenheimer in general covariant tetrad form. Maxwell equations in Riemann space can be presented as one matrix equation [106], [126], [127]…”

Section: Approximations Influencing Physical Resultsmentioning

confidence: 99%

On exact solutions for quantum particles with spin S = 0, 1/2, 1 and de Sitter event horizon

Red'kov

Ovsiyuk

2010

Ricerche mat.

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Exact wave solutions for particles with spin 0, 1/2 and 1 in the static coordinates of the de Sitter space-time model are examined in detail. Firstly, for scalar particle, two pairs of linearly independent solutions are specified explicitly: running and standing waves. A known algorithm for calculation of the reflection coefficient R j on the background of the de Sitter space-time model is analyzed. It is shown that the determination of R j requires an additional constrain on quantum numbers ρ/hc j, where ρ is a curvature radius. When taken into account of this condition, the R j vanishes identically. It is claimed that the calculation of the reflection coefficient R j is not required at all because there is no barrier in an effective potential curve on the background of the de Sitter space-time. The same conclusion holds for arbitrary particles with higher spins, it is demonstrated explicitly with the help of exact solutions for electromagnetic and Dirac fields.

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Section: Approximations Influencing Physical Resultsmentioning

confidence: 99%

On exact solutions for quantum particles with spin S = 0, 1/2, 1 and de Sitter event horizon

Red'kov

Ovsiyuk

2010

Ricerche mat.

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“…Below we use the complex formalism of Riemann -Silberstein -Majorana -Oppenheimer in Maxwell electrodynamics extended to the case of arbitrary pseudo-Riemannian space -time in accordance with the tetrad recipe of Tetrode -Weyl -Fock -Ivanenko (for more detail, see [167,168]).…”

Section: -Dimensional Form Of the Wave Equationmentioning

confidence: 99%

Spherical waves of spin 1 particle in anti de Sitter space-time

Ovsiyuk,

Red'kov

2011

Preprint

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Three possible techniques to deal with a vector particle in the anti de Sitter cosmological model are viewed: Duffin -Kemmer -Petiau matrix formalism based on the general tetrad recipe, group theory 5-dimensional approach based on the symmetry group SO(3.2), and a tetrad form of Maxwell equations in complex Riemann -Silberstein -Majorana -Oppenheimer representation. In the first part, a spin 1 massive field is considered in static coordinates of the anti de Sitter space-time in tetrad-based approach. The complete set of spherical wave solutions with quantum numbers (ǫ, j, m, l) is constructed; angular dependence in wave functions is described with the help of Wigner functions. The energy quantization rule has been found. Transition to massless case of electromagnetic field is specified, and electromagnetic solutions in Lorentz gauge have been constructed. In the second part, the problem of a particle with spin 1 is considered on the base of 5-dimensional wave equation specified in the same static coordinates. In the third part, a rarely used approach, based on tetrad form of Maxwell equations in complex representation is examined in the anti de Sitter model.

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“…Recalling that, by definition, the radius vector x from the source, located at the origin, to the field point is x = |x|n n n , we note that B ⊥ · · · x = 0 and x × × ×n n n = 0, which simplifies Eqn. (41) to…”

Section: The Paraxial Approximationmentioning

confidence: 99%

The physics of angular momentum radio

Thidé

Tamburini

2015

2015 1st URSI Atlantic Radio Science Conference (URSI AT-RASC)

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To this day, wireless communications, as well as radio astronomy and other radio science and technology applications, have made predominantly use of techniques built on top of the electromagnetic linear momentum physical layer. As a supplement and/or alternative to this conventional approach, techniques rooted in the electromagnetic angular momentum (moment of momentum) physical layer have been advocated, and promising results from proof-of-concept laboratory and real-world angular momentum wireless and fiber communication experiments were recently reported. A physical observable in its own right, albeit much more sparingly used than other electromagnetic observables such as energy and linear momentum, the angular momentum exploits the rotational symmetry of the electromagnetic field and the rotational (spinning and orbiting) dynamics of the pertinent charge and current densities. Here we present a review of the fundamental physical properties of the electromagnetic angular momentum observable, derived from the fundamental postulates of classical electrodynamics (the Maxwell-Lorentz equations), and put it into its context among the other Poincaré symmetry invariants of the electromagnetic field. The multi-mode quantized character and other physical properties that sets the classical electromagnetic angular momentum apart from the electromagnetic linear momentum are pointed out. We give many of the results both in terms of the electric and magnetic field vectors and in terms of the complex Riemann-Silberstein vector formalism (Majorana-Oppenheimer representation of classical electrodynamics) and discuss formal parallels with first quantization formalism. We introduce generalized and symmetrized extensions of the Jefimenko integral formulas for calculating exact expressions for the electric and magnetic fields directly from arbitrary given electric and/or magnetic source distributions and use them for deriving expressions for the volumetric density of the electromagnetic angular momentum radiated from any given arbitrary localized distribution of charges and currents. Our results generalize earlier results, obtained by other authors for certain specific configurations only, and facilitate the modeling and design of angular momentum transducers. They show that the volume integrated angular momentum density, i.e., the total angular momentum emitted by the sources, always tends asymptotically to a constant when the distance from the source volume tends to infinity, proving that a radiation arrow of time exists also for angular momentum, as it does for linear momentum (the volume integrated Poynting vector). Consequently, angular momentum physics (torque action) offers an alternative or a supplement to linear momentum physics (force action) as a means of transferring information wirelessly over very long distances. This finding opens possibilities for, among other things, a more flexible utilization of the radio frequency spectrum and paves the way for the development of new information transfer techniques. We discuss ...

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Maxwell equations in complex form of Majorana–Oppenheimer, solutions with cylindric symmetry in Riemann S 3 and Lobachevsky H 3 spaces

Cited by 13 publications

References 14 publications

On exact solutions for quantum particles with spin S = 0, 1/2, 1 and de Sitter event horizon

On exact solutions for quantum particles with spin S = 0, 1/2, 1 and de Sitter event horizon

Spherical waves of spin 1 particle in anti de Sitter space-time

The physics of angular momentum radio

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